Can you simulate many coin flips by rolling a single funky die?

We're used to dice being "fair": each side lands with the same probability. But take any rigid object (say, a plastic mug) and toss it in the air—there are several different ways it can land, but with different probabilities. For instance, it might land more often on its side than directly on its bottom. In this sense, all rigid obejcts are "dice," but with unfair or uneven probabilities. So, it's natural to ask: how could I *design* a shape that has specific, target probabilities? For instance, maybe I want a single die that simulates the probability of flipping several coins—or the sum of two ordinary 6-sided die. Alternatively, I might ask for a funky shape (resembling, say, a dragon) that has fair statistics. This project develops tools to do exactly that: given an initial shape, it tries to find the minimal change to the shape so that it achieves a given set of probabilities. The project is described in the paper Baktash, Sharp, Zhou, Crane, Jacobson "Putting Rigid Bodies to Rest" ACM Transactions on Graphics/SIGGRAPH 2025 Find out more at https://hbaktash.github.io/projects/putting-rigid-bodies-to-rest/index.html